Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
499971 | Computer Methods in Applied Mechanics and Engineering | 2007 | 13 Pages |
Abstract
A Legendre and Chebyshev dual-Petrov–Galerkin method for hyperbolic equations is introduced and analyzed. The dual-Petrov–Galerkin method is based on a natural variational formulation for hyperbolic equations. Consequently, it enjoys some advantages which are not available for methods based on other formulations. More precisely, it is shown that (i) the dual-Petrov–Galerkin method is always stable without any restriction on the coefficients; (ii) it leads to sharper error estimates which are made possible by using the optimal approximation results developed here with respect to some generalized Jacobi polynomials; (iii) one can build an optimal preconditioner for an implicit time discretization of general hyperbolic equations.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Jie Shen, Li-Lian Wang,